Unit A Homework

Homework
Geometry & Probability
Unit A
Name
Date
Period
Lesson 10 – Surface Area of Prisms
The sum of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. The
surface area S.A. of a rectangular prism with length , width w, and height h is the sum of the areas of its
faces. S.A. = 2 w + 2 h + 2wh
Examples
Find the surface area of the rectangular prism. Faces Area
3 cm
4 m
3 cm
3 m
7 cm
2 m
2 m
4.9 ft
top and bottom 2 (4 · 3) = 24
front and back 2 (4 · 2) = 16
two sides 2 (2 · 3) = 12
sum of the areas 24 + 16 + 12 = 52
Alternatively, replace with 4, w with 3,
and h with 2 in the formula for surface area.
S. A. = 2 w + 2 h + 2wh
= 2 (4 · 3) + 2 (4 · 2) + 2 (3 · 2)
= 24 + 16 + 12
= 52
So, the surface area of the rectangular prism is 52 square meters.
4 m
back
4 m
2 m
side bottom side
2 m
3 m
front
top
3 m
Exercises
Find the surface area of each prism. Show your work.
1. _________________ 2. _________________ 3. _________________
3 ft
0.7 ft
8 mm
15 mm
17 mm
9 mm
4. _________________
CONTAINERS A company needs to package hazardous chemicals in special plastic rectangular prism
containers that hold 80 cubic feet. Find the whole number dimensions of the container that would use the
least amount of plastic.